| Exam Board | AQA |
|---|---|
| Module | M2 (Mechanics 2) |
| Year | 2007 |
| Session | January |
| Marks | 8 |
| Paper | Download PDF ↗ |
| Mark scheme | Download PDF ↗ |
| Topic | Work done and energy |
| Type | Work done against friction/resistance - inclined plane or slope |
| Difficulty | Moderate -0.8 This is a straightforward application of conservation of energy and work-energy principle with standard values. Part (a) is direct PE to KE conversion, part (b) is recall, and part (c) requires one additional step accounting for work done against resistance. All steps are routine M2 content with no problem-solving insight needed. |
| Spec | 6.02d Mechanical energy: KE and PE concepts6.02e Calculate KE and PE: using formulae6.02i Conservation of energy: mechanical energy principle |
| Answer | Marks | Guidance |
|---|---|---|
| (a) \(\frac{1}{2} \times 35 \times v^2 = 35 \times 9.8 \times 10\) giving \(v = 14 \text{ (ms}^{-1}\text{)}\) | M1, A1, A1 | Energy method |
| (b) Air resistance or friction | B1 |
| Answer | Marks | Guidance |
|---|---|---|
| Work done: \(F \times 20 = 910\), so \(F = 45.5 \text{ (N)}\) | M1, A1, m1, A1 | Difference attempted ±; \(F > 0\) |
**(a)** $\frac{1}{2} \times 35 \times v^2 = 35 \times 9.8 \times 10$ giving $v = 14 \text{ (ms}^{-1}\text{)}$ | M1, A1, A1 | Energy method | **Total: 3 marks**
**(b)** Air resistance or friction | B1 | | **Total: 1 mark**
**(c)** Energy lost = $35 \times 9.8 \times 10 - \frac{1}{2} \times 35 \times 12^2 = 910$
Work done: $F \times 20 = 910$, so $F = 45.5 \text{ (N)}$ | M1, A1, m1, A1 | Difference attempted ±; $F > 0$ | **Total: 4 marks**
**Question 1 Total: 8 marks**
---1 A child, of mass 35 kg , slides down a slide in a water park. The child, starting from rest, slides from the point $A$ to the point $B$, which is 10 metres vertically below the level of $A$, as shown in the diagram.\\
\includegraphics[max width=\textwidth, alt={}, center]{480a817d-074f-440d-829e-c8f8a9746151-2_259_595_685_705}
\begin{enumerate}[label=(\alph*)]
\item In a simple model, all resistance forces are ignored.
Use an energy method to find the speed of the child at $B$.
\item State one resistance force that has been ignored in answering part (a).
\item In fact, when the child slides down the slide, she reaches $B$ with a speed of $12 \mathrm {~m} \mathrm {~s} ^ { - 1 }$.
Given that the slide is 20 metres long and the sum of the resistance forces has a constant magnitude of $F$ newtons, use an energy method to find the value of $F$.\\
(4 marks)
\end{enumerate}
\hfill \mbox{\textit{AQA M2 2007 Q1 [8]}}